Networks for Fixed Media

The genesis of Networks comes out of a desire to prove the efficacy of composition with Klumpenhouwer Networks (K-nets). It is my belief that for the post-tonal composer looking for a happy medium between strict formal procedures such as serialism (which is, apparently, outmoded in this day and age) and completely free post-tonality loosely governed by an intuitive set-theoretic approach, K-nets offer exactly this happy medium.

Rather than focusing on sets as fixed objects, K-nets focus the composer’s attention on transformations. Composition with K-nets means a post-tonal music that is governed, regulated and unified on the one hand, but which places its emphasis on motion and transformation rather than on the stasis of fixed sets or unchanging row forms.

The specific networks used for the composition of Networks come from an article I wrote for the Journal of Schenkerian Studies entitled “Post-Tonal Hierarchization in Wozzeck.” In Wozzeck I discovered a Tonnetz of K-nets at work, unifying together on one grid the 37 sets defined as salient to Wozzeck by Allen Forte. On this Tonnetz, which I call a K-Tonnetz, every four-square box is superisographic with every other foursquare box (for a definition of K-net superisography, one should consult the article); furthermore, all the pentachords, hexachords, septachords and octachords described by Forte as salient are findable as adjacencies on the K-Tonnetz.

So I use this Wozzeck K-Tonnetz as my pre-compositional harmonic landscape for Networks. Any foursquare K-net on the K-Tonnetz is available to me, in any transposition, as is every identified pentachordal, hexachordal, septachordal or octachordal adjacency, in any transposition, that is superisographic to the parent hexachord, which is a 6-31 omnibus governing sonority of Wozzeck. (It should be noted that Perle would never have called it a 6-31 sonority, but they did agree that this sonority was of great importance, and if those two agreed on anything, there was probably something to it.) Transposition away from the parent K-Tonnetz denotes a hierarchically inferior set, giving the composer a means of post-tonal hierarchization. (For more details on why this is so, again, consult the article.)

The K-Tonnetze identified as governing Wozzeck and also used as a pre-compositional device for Networks are given below.

Next, it would be remiss not to address the issue of the medium for which Networks is composed. Like Diogenes looking for an honest man, I had been looking for years for an elder statesperson to guide me in my career goals which are frankly more concerned with being a composer/thinker and a composer-theorist hyphenate than they are with having the Big Composition Career (capital letters intended). I lament what seems to be the paucity of ideas in today’s concert music establishment landscape. Where are the heirs apparent to Babbitt and to Perle? Where are the essayist composers who are having the Big Careers (capital letters intended again)? Where are the Arthur Bergers and (whether one agrees with his assessments or not) the George Rochbergs?

So it has been my pleasure to have become reacquainted recently with the work of Benjamin Boretz. Realizing that I had been tardy for some time in my intention to compose a self-conscious K-net piece, I came across Boretz’s fixed media piece Group Variations (or, more properly, Group Variations II). This piece is based on an acoustic version for large chamber ensemble (Group Variations I). The piece is very dense and complex, and probably defies human performance realization. The turn to the electronic medium was understandable for Boretz.

I got to thinking, whatever happened to pitch-determinate pieces for fixed media? This too seems to be a lost art. Where are today’s Group Variations, today’s Philomel? This criticism is not to be taken with anything less than a heaping tablespoon of salt: the current state of affairs in electronic music is marvelous. So much is possible. But when so much is possible, it seems as though some of the fundamentals have gotten lost. Contemporary fixed media pieces strike me as approaching an all-texture-all-the-time sort of affair.

So I thought it might be refreshing to try to compose a pitch-determinate piece for fixed media, as a successor to Group Variations and to Philomel. I conceived of the piece as an ensemble piece: an ensemble comprised of ten pitch-determinate sounds that have analogues to acoustic music instrumentation. I chose ten sounds in my sound bank that are abstract enough not to directly imitate the intended analogue instrument (most direct samples of instruments are dreadful) but which behave in some analogous way to the intended analogue. (The one exception is the contrabass sample which I used, intact, which I think is quite good.) The analogue (analog?) instruments are wind quintet and string quintet. The piece could conceivably be performed by this standard ensemble, if the ensemble can achieve some of the more complex polyrhythms and subdivisions that exist therein.

That said, the piece is a fixed media piece in its own right for determinately composed pitches and rhythms. It owes greatly both to Berg and to Boretz, and it is hoped here that it is a worthy tribute to both of them.